ON A CLASSIFICATION OF PRIME RINGS
作者:
J.G. Raftery,
J.E. van den Berg,
期刊:
Quaestiones Mathematicae
(Taylor Available online 1992)
卷期:
Volume 15,
issue 2
页码: 139-150
ISSN:1607-3606
年代: 1992
DOI:10.1080/16073606.1992.9631680
出版商: Taylor & Francis Group
关键词: 16A12;16A63
数据来源: Taylor
摘要:
Letmbe a positive cardinal. We denote by Pr(m) (resp.Pt(m)) the class of all ringsRfor whichmis the least cardinal such that all nonzero elements ofRpossess right (resp. left) insulators of cardinality less than m + 1. We also setPr(m) = Un≤ m Pr(n). The classes Pr(m),>m0, partition the class of all prime rings. Various descriptions of these classes are obtained. In particular ifmis regular thenPr(m) contains just those ringsRsuch thatt(R) = 0 for all proper torsion preradicalston Mod -Rwhose torsion classes are closed under direct products of fewer than m modules. Examples are provided which show thatPr(m) is non-empty for all m > 0 and which partially answer the question: for which cardinalsm,nisPr(m) ∩Pt(n) nonempty?
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